Name: Anonymous 2007-08-30 13:43 ID:eUFPtE+p
I enjoyed those two Monsieur Ejemplé threads so I thought I'd pose a maths question of my own, in fact I'll do two on countability. They're not that hard, but I think they're more enjoyable than calculus
1. Let f : R -> R be monotonic.
Is the set { x | f is discontinous at x} countable?
where x is in R.
2. A function f : N -> N is increaing if f(n)>= f(n+1) (if it's bigger than OR equal to) and a decreasing function is similarly defined.
is the set {f | f is increasing} countable?
is the set {f | f is decreasing} countable?
1. Let f : R -> R be monotonic.
Is the set { x | f is discontinous at x} countable?
where x is in R.
2. A function f : N -> N is increaing if f(n)>= f(n+1) (if it's bigger than OR equal to) and a decreasing function is similarly defined.
is the set {f | f is increasing} countable?
is the set {f | f is decreasing} countable?